CR-twistor spaces over manifolds with G2 - and Spin(7)-structures
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00572817" target="_blank" >RIV/67985840:_____/23:00572817 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10231-023-01307-0" target="_blank" >https://doi.org/10.1007/s10231-023-01307-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10231-023-01307-0" target="_blank" >10.1007/s10231-023-01307-0</a>
Alternative languages
Result language
angličtina
Original language name
CR-twistor spaces over manifolds with G2 - and Spin(7)-structures
Original language description
In 1984 LeBrun constructed a CR-twistor space over an arbitrary conformal Riemannian 3-manifold and proved that the CR-structure is formally integrable. This twistor construction has been generalized by Rossi in 1985 for m-dimensional Riemannian manifolds endowed with a (m- 1) -fold vector cross product (VCP). In 2011 Verbitsky generalized LeBrun’s construction of twistor-spaces to 7-manifolds endowed with a G 2-structure. In this paper we unify and generalize LeBrun’s, Rossi’s and Verbitsky’s construction of a CR-twistor space to the case where a Riemannian manifold (M, g) has a VCP structure. We show that the formal integrability of the CR-structure is expressed in terms of a torsion tensor on the twistor space, which is a Grassmannian bundle over (M, g). If the VCP structure on (M, g) is generated by a G 2- or Spin (7) -structure, then the vertical component of the torsion tensor vanishes if and only if (M, g) has constant curvature, and the horizontal component vanishes if and only if (M, g) is a torsion-free G 2 or Spin (7) -manifold. Finally we discuss some open problems.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annali di Matematica Pura ed Applicata
ISSN
0373-3114
e-ISSN
1618-1891
Volume of the periodical
202
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
23
Pages from-to
1931-1953
UT code for WoS article
000934589900001
EID of the result in the Scopus database
2-s2.0-85147737670